Hi Heidi, it is currently not possible for attendees to chat with other attendees; however, organizers/panelists responding to questions do have the option to "Respond to all" when answering to questions, rather than responding privately to the individual asking the question.
The main reason chat is not included for GoToWebinar attendees is because you could potentially have a two thousand person audience. Allowing attendees to chat could violate some privacy rules of certain organizations, and also greatly distract audience members. We do have Chat available for up to 200 attendees however, with GoToTraining, and 100 attendees with GoToMeeting if you feel that you need this function for your broadcasts to smaller audiences.
You can send a chat message through the GoToWebinar interface addressed to the entire audience.
Chat its self was designed for staff members, while 'Questions' were designed for attendees to enter them and Organizers to manage this potentially large list in their Attendee Questions pane.